SOLUTION: The hypotenuse of a right triangle is 8 ft. longer than one leg and 4 ft. longer than the other leg. What are the dimensions of this triangle? Show the equation you used to solve t

Question 128479: The hypotenuse of a right triangle is 8 ft. longer than one leg and 4 ft. longer than the other leg. What are the dimensions of this triangle? Show the equation you used to solve this and then your answer.

Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Let c = the hypotenuse and a and b the other two legs.
From the problem description, you can write:
and Rewrite these in terms of a and b to get:
and Now you can use the Pythagorean theorem to find c, the hypotenuse:
Substitute the two equations above for a and b:
Simplify.
Combine like-terms.
Subtract from both sides.
Solve this quadratic by factoring:
, so then...
or Discard the first solution as c must be greater than 8 or else you have one leg of the triangle equal to zero!
So, the hypotenuse is 20 and the other two legs are a=12 and b = 16.
Check:
Substitute c = 20, a = 12, and b = 16.

OK!
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